The sum of the ages of ahsan and his mother is 61 years.The difference in their ages is 29 years.By forming a pair of simultaneous linear equations,find (i)ahsan's present age (ii)the age of ahsan's mother when ahsan is 21 years old

Answer:

The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.

Step-by-step explanation:

The diagram of the situation described is shown in the attached image.

The distance of the boat to the dock along the water level at any time is x

The distance from the person on the dock to the boat at any time is y

The height of the dock is 5 ft.

These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.

According to Pythagoras' theorem

y² = x² + 5²

y² = x² + 25

(d/dt) y² = (d/dt) (x² + 5²)

2y (dy/dt) = 2x (dx/dt) + 0

2y (dy/dt) = 2x (dx/dt)

When the boat is 4 ft from dock, that is x = 4 ft,

The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s

The speed with which the boat is approaching the dock = (dx/dt)

Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock

When the boat is 4 ft from the dock, x = 4 ft.

And we can obtain y at that point.

y² = x² + 5²

y² = 4² + 5² = 16 + 25 = 41

y = 6.40 ft.

So, to the differential equation relation

2y (dy/dt) = 2x (dx/dt)

when x = 4 ft,

y = 6.40 ft

(dy/dt) = 2 ft/s

(dx/dt) = ?

2 × 6.40 × 2 = 2 × 4 × (dx/dt)

25.6 = 8 (dx/dt)

(dx/dt) = (25.6/8) = 3.20 ft/s.

Hope this Helps!!!

Answer:  D) 8 inches

====================================================

Work Shown:

Refer to the diagram below.

A = 50 degrees

B = unknown

C = 80 degrees

-----

For any triangle, the three angles always add to 180

A+B+C = 180

50+B+80 = 180

B+130 = 180

B = 180-130

B = 50 degrees

Since angles B and C are the same measure, their opposite sides are the same length. Triangle ABC is isosceles. Therefore, a = x = 8

Answer: D) 8 inches.

Step-by-step explanation: The triangle has three angles: two were given (50º and 80º) and the other one can be calculated (50º). Therefore, this triangle is an isosceles triangle, it has one base and two congruent sides. Since the one side is 8in, then the other missing side must also be 8in according to the Isosceles Triangle Theorem.

Answer:

[tex]h = \frac{s - 2ar}{2ar} \\ [/tex]

Step-by-step explanation:

[tex]s = 2ar + 2arh \\ s - 2ar = 2arh \\ \frac{s - 2ar}{2ar} = \frac{2arh}{2ar} \\ h = \frac{s - 2ar}{2ar} [/tex]

hope this helps you

brainliest appreciated

good luck! have a nice day!

Answer:

2

Step-by-step explanation:

Scale Factor = [tex]\frac{AnySideOfDiagram}{AnySideOfMP3Player}[/tex]

So,

Scale Factor = [tex]\frac{8}{4} = \frac{14}{7}[/tex] = 2

So,

The scale factor is 2

Answer:

25/88

Step-by-step explanation:

25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles

P(red) = number of red/total

          = 25/88

Answer:

Dear user,

Answer to your query is provided below

Probability of choosing a red marble is 0.28 or (25/88)

Step-by-step explanation:

Total number of marbles = 88

Number of red marbles = 25

Probability = 25/88

Answer:

the correct answer is

Step-by-step explanation:

So, the probability is:P(greater than 4)=26=13. This is a theoretical probability, which is the observed number of favorable outcomes out of a certain number of trials. For instance, suppose you rolled the six-sided die five times, and got the following results:2,6,4,5,6

hope this help you!!!!!

Answer:

1/5 chance.

Step-by-step explanation:

There is only one number, 5, that is greater than 4 and there are 5 total numbers so there is a 1/5 chance selecting that number.

Answer:

216-343

Step-by-step explanation:

the number 312 lies between 125 and 330

Answer:

Step-by-step explanation:

[tex]\sqrt{x-2}+8=x\\\\\sqrt{x-2}=x-8\\[/tex]

Square both sides,

[tex]x-2=(x-8)^{2}\\\\x-2=x^{2}-2*x*8+8^{2}\\\\x-2=x^{2}-16x+64\\\\x^{2}-16x+64=x-2\\\\x^{2}-16x+64-x+2=0\\\\x^{2}-17x+66=0[/tex]

Sum = - 17

Product = 66

Factors = -6 , -11

x² - 6x -11x + (-6)*(-11) = 0

x(x - 6) -11(x - 6) = 0

(x-6) (x - 11) = 0

x -6 = 0   ; x - 11 = 0

x = 6   ; x =11

Here,  x = 6 is a extraneous solution

Answer:

Tangent

Step-by-step explanation:

if the angle in question is the bottom of the ladder and the ground, then tangent is opposite over adjacent... or 12/5

Hope this is right

Answer:

Step-by-step explanation:

The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...

  (6 days/week)($1.10/day) = $6.60/week

The three laborers working 50 weeks/year will have a labor cost of ...

  (3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year

__

In the US, the labor charge per person per week is ...

  (14 hr/day)(6 day/week) = 84 hr/week

That's 40 hours of straight pay and 44 hours of overtime pay, or ...

  7.25(40 +1.5(44)) = 7.25(106) = 768.50

For 150 person-weeks per year, the total US labor charge is ...

  ($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year

__

The materials cost for a year is ...

  ($50/rug)(12 rugs/year) = $600/year

__

The revenue is ...

  ($2000/rug)(12 rugs/year) = $24,000/year

Profit is the difference between revenue and the total of costs:

  profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia

__

So, the table gets filled as follows:

  (labor, material, fixed cost, revenue, profit)

Mongolian-made

  ($990, $600, $10000, $24000, $12410)

US-made

  ($115275, $600, $10000, $24000, -$101,875)

The US labor cost would be $115,275.

_____

Comment

For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.

Answer:

0.2613

Step-by-step explanation:

Use binomial probability.

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

P = ₇C₂ (0.6)⁵ (0.4)²

P = 0.2613

Answer:

1/26

Step-by-step explanation:

There is 1 four of spades, and 1 ace of clubs.

So the probability is 2/52, or 1/26.

Answer:

P(four of spades or ace of clubs)= 1/26

Step-by-step explanation:

In a deck of 52 cards, there is one four of spaces and one ace of clubs. we want to find the probability of selecting those cards.

P(four of spades or ace of clubs)=four of spades+ace of clubs/total cards

There is 1 four of spades and 1 ace of clubs. 1+1=2

P(four of spades or ace of clubs)=2/total cards

There are 52 total cards in a deck.

P(four of spades or ace of clubs)=2/52

This fraction can be simplified. Both the numerator (top number) and denominator (bottom number) can be divided by 2.

P(four of spades or ace of clubs)= (2/2) / (52/2)

P(four of spades or ace of clubs)= 1/26

Answer:

0.77777777777...

Step-by-step explanation:

7/9 = 7 divided by 9

7 divided by 9 = 0.77777777777...

Reflect over y-axis,reflect over the X axis ,rotate 180°

Option D is the correct option.

Explanation:

Let's take point A which is (4,-1)

Reflection over y- axis will make this point (4,1)

Then, reflection over X axis will make this point (4,-1)

After rotation of 180 degree we will get (-4,1) .

Please see the attached picture....

Hope it helps...

Good luck on your assignment...

Answer:  d) reflect over the x-axis, reflect over y-axis, rotate 180°

Step-by-step explanation:

A reflection over the x-axis and a reflection over the y-axis is the SAME as a rotation of 180°. Together they make a rotation of 360°, which results in the image staying at the same place.

Reflection over the x-axis changes the sign of the y-coordinate

Z = (x, y)    →    Z' = (x, -y)

Reflection over the y-axis changes the sign of the x-coordinate

Z' = (x, -y)    →    Z'' = (-x, -y)

Rotation of 180° changes the signs of both the x- and y-coordinates

Z'' = (-x, -y)   →     Z''' = (x, y)

Answer:

C

Step-by-step explanation:

3x+2-x>8

2x+2>8

2x>8-2

2x>6

x>3

Answer:

C

Step-by-step explanation:

Answer:

(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b) The expected number of available places when the limousine departs is 0.338.

Step-by-step explanation:

Let the random variable Y represent the number of passenger reserving the trip shows up.

The probability of the random variable Y is, p = 0.70.

The success in this case an be defined as the number of passengers who show up for the trip.

The random variable Y follows a Binomial distribution with probability of success as 0.70.

(a)

It is provided that n = 6 reservations are made.

Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:

P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)

[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]

Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b)

The formula to compute the expected value is:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]

Compute the expected number of available places when the limousine departs as follows:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

         [tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]

Thus, the expected number of available places when the limousine departs is 0.338.

Answer:

Y = -X - 7

Step-by-step explanation:

y-y1 =m(x-x1)

y-(-2)= -1(x-(-5)

y+2 = -1(x+5)

Solve for y

subtract 2 from both sides

y=-x-5-2

Y = -x-7

Answer:

(C)12 Units

Step-by-step explanation:

Triangle WRS has points W(0, -1), R(1.75, 1.5), and S(5, -1).

[tex]WR=\sqrt{(1.75-0)^2+(1.5-(-1))^2}=\dfrac{\sqrt{149}}{4}[/tex]

[tex]WS=\sqrt{(5-0)^2+(-1-(-1))^2}=\sqrt{25}=5[/tex]

[tex]RS=\sqrt{(5-1.75)^2+(-1-1.5)^2}=\dfrac{\sqrt{269}}{4}[/tex]

Perimeter of Triangle WRS

[tex]= \dfrac{\sqrt{149}}{4}+5+\dfrac{\sqrt{269}}{4}\\\approx 12$ Units[/tex]

Answer:

c

Step-by-step explanation:

took it on edge

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of

weekend guest bills to test the manager’s claim.

a. Which form of the hypotheses should be used to test the manager’s claim? Explain.

1) H0:μ ≥ 600

Ha:μ < 600

2) H0:μ ≤ 600

Ha:μ > 600

3) H0:μ=600

Ha:μ≠600

b. What conclusion is appropriate when H0 cannot be rejected?

c. What conclusion is appropriate when H0 can be rejected?

Solution:

a) the hypotheses should be used to test the manager’s claim is

H0:μ ≤ 600

Ha:μ > 600

This is because the already known or assumed mean guest bill for a weekend is 600 or less. This forms the null hypothesis. The alternative is the opposite of the null hypothesis. Since the alternative states that it is increasing, the sign,> would be used.

b) If H0 cannot be rejected, it means that there is no sufficient evidence to reject H0 at the given level of significance.

c) if H0 can be rejected, it means that there is sufficient evidence to reject H0 at the given level of significance.

Answer:

Your correct answer is 31/50 + -4/25 i

Step-by-step explanation:

5+4i/6+8i = 31/50 + -4/25 i

Answer:

The answer is C.

Step-by-step explanation:

[tex]50-x^2=0[/tex]

[tex]x^2=50[/tex]

[tex]x=\pm \sqrt{50} =\pm \sqrt{25*2}=\pm 5\sqrt{2}[/tex]

The answer is C (I am assuming that it isn't 5/2).

When x = 1, the expression evaluates to 2/3.

When x = 4/9, the expression evaluates to 1.

When x = 1 1/3, the expression evaluates to 3/5.

Let's evaluate the expression 4/15 ÷ x + 0.4 for each given value of x.

1) When x = 1:

4/15 ÷ 1 + 0.4 = 4/15 + 0.4 = 4/15 + 6/15 = 10/15 = 2/3

So, when x = 1, the expression evaluates to 2/3.

2) When x = 4/9:

4/15 ÷ (4/9) + 0.4 = 4/15 * (9/4) + 0.4 = 36/60 + 0.4 = 3/5 + 0.4 = 3/5 + 2/5 = 5/5 = 1

So, when x = 4/9, the expression evaluates to 1.

3) When x = 1 1/3 (or 4/3):

4/15 ÷ (4/3) + 0.4 = 4/15 * (3/4) + 0.4 = 12/60 + 0.4 = 1/5 + 0.4 = 1/5 + 2/5 = 3/5

So, when x = 1 1/3, the expression evaluates to 3/5.

Learn more about expression here

https://brainly.com/question/16922619

#SPJ2

Answer:

a) Option D is correct.

H0​: μ = 71

Ha​: μ > 71

b) Option F is correct

z > 1.28

c) z = 2.85

d) Option C is correct.

Reject H0.There is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.

Step-by-step explanation:

a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

This question aims to test the the true mean heart rate during laughter exceeds 71 beats per minute.

Hence, the null hypothesis is that there isn't sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute. That is, the true mean doesn't exceed 71 beats per minute.

And the alternative hypothesis is that there is sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute.

Mathematically,

The null hypothesis is represented as

H₀: μ = 71

The alternative hypothesis is represented as

Hₐ: μ > 71

b) Using z-distribution, the rejection area is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction,

Significance level = (100% - confidence level)/2

0.10 = 10% = (100% - confidence level)/2

20% = 100% - (confidence level)

Confidence level = 100% - 20% = 80%

Critical value for 80% confidence level = 1.28

And since we are testing if the true mean heart rate during laughter exceeds 71 beats per minute, the rejection area would be

z > 1.28

c) The test statistic is given as

z = (x - μ)/σₓ

x = sample mean = 73.4

μ = 71

σₓ = standard error = (σ/√n)

σ = 8

n = Sample size = 90

σₓ = (8/√90) = 0.8433

z = (73.4 - 71) ÷ 0.8433

z = 2.846 = 2.85

d) Since the z-test statistic obtained, 2.85, is firmly in the rejection area, z > 1.28, we reject the null hypothesis, accept the alternative hypothesis and say that there is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.

Hope this Helps!!!

Answer:

A) 715 ways

B) 715 ways

C) (1/715)

Step-by-step explanation:

This is a permutation and combination problem.

Since we want to select a number of people from a larger number of people, we use combination as the order of selection isn't important now.

A) How many different ways can the officers be appointed?

There are 4 officer positions.

There are 13 people in total.

We want to select 4 people from 13

Number of ways to select 4 people from 13 = ¹³C₄ = 715

B) How many different ways can the committee be appointed?

Number of committee members = 4

Total number of people available = 13

Number of ways to select 4 people from 13 = ¹³C₄ = 715

C) What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?

Selecting a group of the youngest candidates is just 1 amongst the total number of ways the 4 committee members can be picked,

Hence, the required probability = (1/715)

Hope this Helps!!!

An angle is the intersection of two noncollinear rays at a common endpoint. The rays are called sides and the common endpoint is called the vertex.

Answer:

The answer is nothing duh

Step-by-step explanation:

Answer:

Step-by-step explanation:

max can be found by the formula:

t=-b/2a

t=-9.8/2*(-4.9)

t=-9.8/-9.8

t=1

1 sec

to find maximum height obtained we find the vertex:

plug in 1 for t and simply solve:

h(t)= -4.9t^2 + 9.8t + 1

h(t)= -4.9*1^2 + 9.8*1 + 1

h(t)= -4.9*1 + 9.8 + 1

h(t)= -4.9 + 10.8

h(t)= 5.9

height is 5.9

Answer:

P(33) = 0.0826

Step-by-step explanation:

The binomial distribution in this case has parameters n=55 and p=0.55.

The probability that k successes happen with these parameters can be calculated as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}\\\\\\[/tex]

We have to calculate the probability fo X=33 succesess.

This can be calculated using the formula above as:

[tex]P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826\\\\\\[/tex]